# Space, shape and measurement: Use the Cartesian co-ordinate system to derive and apply equations ### Subject outcome

Subject outcome 3.2: Use the Cartesian co-ordinate system to derive and apply equations ### Learning outcomes

• Use the Cartesian co-ordinate system to derive the equation of a line through two given points.
• Use the Cartesian co-ordinate system to derive the equation of a line parallel or perpendicular to another line.
• Use the Cartesian co-ordinate system to derive and use the angle of inclination of a line. ### Unit 1 outcomes

By the end of this unit you will be able to:

• Use the Cartesian co-ordinate system to derive the equation of a line through two given points using:
• the two-point form ### Unit 2 outcomes

By the end of this unit you will be able to:

• Determine the equation of a straight line parallel to another straight line on the Cartesian plane.
• Determine the equation of a straight line perpendicular to another straight line on the Cartesian plane. ### Unit 3 outcomes

By the end of this unit you will be able to:

• Use the gradient of a straight line to determine the angle of inclination of the line with the x-axis.
• Use the angle of inclination to determine the gradient of a straight line. 